Methods and apparatus for determining the location of a shaft within a vessel

ABSTRACT

Apparatus and methods for measuring the amount by which the centerline of a shaft disposed in a vessel is offset from the central vertical axis of the vessel, and for measuring the height of such shaft above the inside bottom of the vessel. Apparatus includes a shaft centerline offset measurement device, a shaft height measurement device, and a control/display console. Each measurement device includes a transducer or optical encoder for sensing a displaced position of a biased plunger to which a code strip is mounted. The devices may be combined into a single shaft offset and height measurement device. Improved methods include calculating shaft offset based on a plurality of readings from the transducer, and applying trigonometric relationships. The apparatus and methods are particularly useful in the verification of paddle or basket shafts utilized in dissolution testing stations, so that the dissolution testing protocol complies with government agency guidelines.

TECHNICAL FIELD

[0001] The present invention generally relates to measurement of thedistance of a shaft from the bottom of a vessel and the amount by whichthe shaft is offset from the center of the vessel. More particularly,the present invention relates to the precise measurement of shaft heightand shaft offset in vessels employed in dissolution testing systems.

BACKGROUND ART

[0002] In the pharmaceutical industry, dissolution testing and analysisis required to be performed on samples taken from batches of tablets orcapsules manufactured by pharmaceutical companies in order to assessefficacy and other properties. Dissolution analysis by automated meanshas become popular for increasing throughput and improving accuracy,precision, reliability, and reproducibility. Automation also relievesthe tedium of manually performing a variety of requisite procedures,including: handling and delivering dosage units such as capsules andtablets; monitoring dissolution system parameters; manipulating theshafts carrying the agitation paddles or sample baskets; recording,displaying and printing accumulated data and test results; and cleaningand filtering the vessels employed in such procedures.

[0003] Despite the benefits accruing from automation, validation of theprocedures employed in dissolution testing and analysis remains acritical consideration. A typical dissolution test requires, among otherthings, that a rotatable shaft equipped with a paddle or basket beproperly positioned in the center of, and properly located a specifieddistance from the bottom of, a dissolution test vessel prior toconducting the test. The USP has promulgated guidelines for thepharmaceutical industry which are enforced by the FDA. Under USP 24,General Chapters, Dissolution (711), the shaft must be positioned suchthat its centerline is not more than 2 mm at any point from the verticalaxis of the vessel, and such that the paddle or basket (typicallymounted to the lower end of the shaft) be positioned at 25 mm±2 mm fromthe bottom of the vessel.

[0004] Various hand-held devices have been utilized to carry out themeasurements required to determine whether a shaft is positioned in adissolution test vessel in compliance with the above-cited guidelines.Rulers, machinist calipers and micrometers, and pass/fail fixturestypify such devices and are known to persons skilled in the art. It isreadily apparent to such skilled persons that operation of these devicesrequires a great deal of manual handling, with critical specificationslargely determined by sight and feel. Conventional shaft measurementdevices therefore engender an unacceptably high risk of error. Thereaccordingly exists a long felt need for improved apparatus and methodsfor determining the position of a shaft installed in the vessel of adissolution testing station.

DISCLOSURE OF THE INVENTION

[0005] In accordance with the present invention, an apparatus ismountable to a shaft disposed within a vessel and is adapted formeasuring the magnitude by which the centerline of the shaft is offsetfrom the central axis of the vessel. The apparatus comprises a housingand a plunger slidably mounted to the housing. The plunger has an outersection extending radially outwardly beyond a wall of the housing, andmeans such as a spring for biasing the plunger radially outwardly. Atransducer is operatively mounted to the housing. The transducer isadapted to encode positions of the plunger and to produce an electricalsignal proportional to a change in position resulting from displacementof the plunger. Means such as data lines are provided for transferringthe signal to means such as a microprocessor for interpreting thesignal.

[0006] In another embodiment according to the present invention, anapparatus is mountable to a shaft having a paddle or basket disposedwithin a vessel. The vessel has a central axis and a hemispherical endregion. The apparatus is adapted for measuring the distance from adistal surface of the paddle or basket to a lowermost point on theinside surface of the hemispherical end region. The apparatus comprisesa housing and a plunger slidably mounted to the housing. The plunger hasan outer section extending outwardly beyond a wall of the housing, andmeans such as a spring for biasing the plunger outwardly. An end portionextends transversely from the plunger beneath the housing and issubstantially centered about a central portion of the housing. Atransducer is operatively mounted to the housing. The transducer isadapted to encode positions of the plunger and to produce an electricalsignal proportional to a change in position resulting from displacementof the plunger. Means such as data lines are provided for transferringthe signal to means such as a microprocessor for interpreting thesignal.

[0007] In another embodiment according to the present invention, asystem is provided for determining the location of a rotatable shaft inrelation to a vessel mounted to a rack of a dissolution testing station.The shaft has a first end mounted to the testing station above thevessel, a second end disposed within the vessel and an operativecomponent secured to the second end. The system comprises a housingincluding means such as a resilient clip and groove for removablymounting the housing to the shaft, and a plunger slidably mounted to thehousing. The plunger has an outer section extending radially outwardlybeyond a wall of the housing and extendable to an inside lateral surfaceof the vessel, and has means such as a spring for biasing the plungerradially outwardly. A transducer is operatively mounted to the housing.The transducer is adapted to encode positions of the plunger, and toproduce an electrical signal proportional to a distance from a referenceposition to an extended position at which the plunger is in contact withthe inside lateral surface of the vessel. Means such as data lines areprovided for transferring the signal to means such as a microprocessorfor interpreting the signal.

[0008] In another embodiment according to the present invention, asystem is provided for determining the location of a rotatable shaft inrelation to a vessel. The vessel has a central axis and a hemisphericalend region, and is mounted to a rack of a dissolution testing station.The shaft has a first end mounted to the testing station above thevessel, a second end disposed within the vessel and an operativecomponent such as a paddle or basket secured to the second end. Thesystem comprises a spherical object removably disposed in a lowermostpoint on an inside surface of the hemispherical end region of thevessel. A housing includes means such as a resilient clip or groove forremovably mounting the housing to the shaft. A plunger is slidablymounted to the housing. The plunger has an outer section extendingbeyond a wall of the housing and extendable to the spherical object, andhas means such as a spring for biasing the plunger outwardly. An endportion has an upper surface and a lower surface, and extendstransversely from the plunger and between the operative component andthe spherical object.

[0009] A transducer is operatively mounted to the housing. Thetransducer is adapted to encode positions of the plunger, and to producean electrical signal proportional to a distance from a referenceposition at which the top surface of the end portion of the plunger isbiased against the operative component to an extended position at whichthe lower surface is in contact with the spherical object. Means such asdata lines are provided for transferring the signal to means such as amicroprocessor for interpreting the signal.

[0010] In another object according to the present invention, a system isprovided for determining the location of a shaft in relation to a vesselin which the shaft is disposed. The vessel has a central axis and ahemispherical end region. The system comprises a shaft offsetmeasurement device which includes a first housing and a first plungerslidably mounted to the first housing. The first plunger has an outersection extending radially outwardly beyond a wall of the first housingand means such as a spring for biasing the first plunger radiallyoutwardly. A first transducer is operatively mounted to the firsthousing. The first transducer is adapted to encode positions of thefirst plunger and to produce a first electrical signal proportional to achange in position resulting from displacement of the first plunger.

[0011] The system further comprises a shaft height measurement devicewhich includes a second housing and a second plunger slidably mounted tothe second housing. The second plunger has an outer section extendingoutwardly beyond a wall of the second housing, and means such as aspring for biasing the second plunger outwardly. An end portion extendstransversely from the second plunger beneath the second housing and issubstantially centered about a central portion of the second housing. Asecond transducer is operatively mounted to the second housing. Thesecond transducer is adapted to encode positions of the second plungerand to produce a second electrical signal proportional to a change inposition resulting from displacement of the second plunger.

[0012] The system further comprises a console including logic means suchas a microprocessor for effecting interpretations of the first andsecond electrical signals and means such as an LCD display fordisplaying the interpretations in human-readable form. Means such asdata lines are provided for transferring the first and second electricalsignals to the logic means.

[0013] In another embodiment according to the present invention, anapparatus is adapted for measuring the magnitude by which the centerlineof a shaft is offset from the central axis of a vessel in which theshaft is disposed, and for measuring the distance from a distal end ofthe shaft to the lowermost point on an inside surface of a hemisphericalend region of the vessel. The apparatus comprises a mounting assembly, alateral plunger slidably mounted to the mounting assembly, a lateraltransducer operatively disposed with respect to the mounting assemblyand to the lateral plunger, a vertical plunger slidably mounted to themounting assembly, and a vertical transducer operatively disposed withrespect to the mounting assembly and to the vertical plunger.

[0014] The lateral plunger has means such as a spring for biasing thelateral plunger radially outwardly. The lateral transducer is adapted toencode positions of the lateral plunger and to produce an electricalsignal proportional to a change in position resulting from displacementof the lateral plunger. The vertical plunger has means such as a springfor biasing the vertical plunger downwardly with respect to the mountingassembly, and includes an upper end portion extending transversely fromthe vertical plunger. The vertical transducer is adapted to encodepositions of the vertical plunger and to produce an electrical signalproportional to a change in position resulting from displacement of thevertical plunger. Means such as data lines are provided for transferringthe signals produced respectively by the lateral and verticaltransducers to means for interpreting the signals. The signalinterpreting means can include a console with which the signaltransferring means communicates, wherein the console has logic meanssuch as a microprocessor for effecting interpretations of the signalsand means such as an LCD display for displaying the interpretations inhuman-readable form.

[0015] The present invention also provides methods for determining theposition of a shaft installed in a vessel with respect to the centralaxis of the vessel and/or lowermost point inside the vessel.

[0016] Accordingly, a method is provided for measuring the amount bywhich the centerline of a shaft is offset from the central axis of avessel in which the shaft is to be disposed, comprising the followingsteps. A measurement device which includes a radially outwardly biasedplunger is mounted to the shaft. The plunger has a settable zeroreference position. The shaft is inserted into the vessel at a normaloperating position of the shaft, wherein a distal end of the plunger isin contact with a lateral inside surface of the vessel at a first distalplunger position. A first displaced plunger position is defined as aposition on the plunger located a distance by which the plunger hasmoved in relation to the zero reference position, the distance beingequal a first displacement magnitude.

[0017] The displacement magnitudes are measured by encoding thedisplaced plunger position and interpreting the displaced plungerposition in relation to the zero reference position, wherein thedisplacement magnitudes determine the shaft centerline offset amount. Avalue for the shaft centerline offset amount is calculated based on themeasured first displacement magnitudes. Finally, a signal is producedwhich is indicative of the shaft centerline offset amount.

[0018] Accordingly, another method is provided wherein a distal end ofthe plunger position is in contact with a lateral inside surface of thevessel at a first distal plunger position. This first displaced plungerposition is reset to the zero reference position. The shaft is thenrotated one full revolution while continuously sampling the displacementof the plunger position is defined as a position on the plunger locateda distance by which the plunger has moved in relation to the zeroreference position, the distance being equal to the displacementmagnitude from this continuous sampling, the lowest and the largestdisplacement magnitudes are kept.

[0019] Another method according to the present invention is formeasuring a shaft height, which is defined as the distance between thedistal end of a shaft and the inside lowermost surface of ahemispherical end region of a vessel in which the shaft is to bedisposed. The method comprises the following steps. A measurement devicewhich includes a downwardly biased plunger is mounted to the shaft. Theplunger includes an end portion. The end portion extends below the shaftand has a predetermined end portion height. A zero reference position ofthe plunger is defined by urging the end portion against the distal endof the shaft. The zero reference position is encoded. The insidelowermost surface of the hemispherical end region of the vessel islocated by inserting a spherical object having a predetermined diameterinto the vessel. The shaft is inserted into the vessel at a normaloperating position of the shaft, permitting the end portion of theplunger to contact the spherical object.

[0020] A displaced plunger position is defined as a position on theplunger located a distance by which the plunger has moved in relation tothe zero reference position in order to contact the spherical object,the distance being equal to a displacement magnitude. The displacementmagnitude is measured by encoding the displaced plunger position andinterpreting the displaced plunger position in relation to the zeroreference position, wherein the sum of a predetermined constant plus thedisplacement magnitude is proportional to the shaft height. A value forthe shaft height is calculated based on the measured displacementmagnitude. A signal is produced which is indicative of the shaft height.

[0021] A further method according to the present invention is formeasuring the amount by which the centerline of a shaft is offset fromthe central axis of a vessel in which the shaft is to be disposed, andfor measuring a shaft height defined as the distance between the distalend of the shaft and the inside lowermost surface of a hemispherical endregion of the vessel. The method comprises the following steps. Theinside lowermost surface of the hemispherical end region of the vesselis located by inserting a spherical object into the vessel. Ameasurement device is mounted over the vessel. The measurement deviceincludes a lateral plunger and a vertical plunger. The vertical plungerincludes an end portion. The shaft is inserted into the vessel at anormal operating position of the shaft.

[0022] A distal end of the lateral plunger is permitted to contact alateral inside surface of the vessel. A displaced lateral plungerposition is defined as a position on the lateral plunger located alateral distance by which the lateral plunger has moved in relation to apredetermined zero reference position of the lateral plunger, thelateral distance being equal to a lateral displacement magnitude. Thelateral displacement magnitude is measured by encoding the displacedlateral plunger position and interpreting the displaced lateral plungerposition in relation to the zero reference position of the lateralplunger, wherein the lateral displacement magnitude determines the shaftcenterline offset amount. A value for the shaft centerline offset amountis calculated based on the measured lateral displacement magnitude. Asignal is produced which is indicative of the shaft centerline offsetamount.

[0023] The end portion of the vertical plunger is permitted to contactthe spherical object. A displaced vertical plunger position is definedas a position on the vertical plunger located a vertical distance bywhich the vertical plunger has moved in relation to a predetermined zeroreference position of the plunger, the vertical distance being equal toa vertical displacement magnitude. The vertical displacement magnitudeis measured by encoding the displaced vertical plunger position andinterpreting the displaced vertical plunger position in relation to thezero reference position of the vertical plunger, wherein the verticaldisplacement magnitude determines the shaft height. A value for theshaft height is calculated based on the measured vertical displacementmagnitude. A signal is produced which is indicative of the shaft height.

[0024] It is therefore an object of the present invention to provide anapparatus for measuring the amount by which the centerline of a shaftdisposed in a vessel is offset from the central vertical axis of thevessel.

[0025] It is another object of the present invention to provide anapparatus for measuring the height of such shaft above the lowermostinside point of the vessel.

[0026] It is a further object of the present invention to provide anapparatus for controlling the process by which the shaft centerlineoffset amount and shaft height are measured, and for expressing theresults of such process using peripheral devices.

[0027] It is yet another object of the present invention to provideimproved methods for determining accurate values for the shaftcenterline offset amount and shaft height.

[0028] Some of the objects of the invention having been statedhereinabove, other objects will become evident as the descriptionproceeds, when taken in connection with the accompanying drawings asbest described hereinbelow.

BRIEF DESCRIPTION OF THE DRAWINGS

[0029]FIG. 1 is a cross-sectional view of a paddle shaft installed in avessel in which the present invention is implemented;

[0030]FIG. 2 is a perspective view of a dissolution testing station inwhich the present invention is implemented;

[0031]FIG. 3A is a perspective view of a shaft centerline offset andheight measurement system according to the present invention;

[0032]FIG. 3B is a perspective view of a shaft height measurement deviceaccording to the present invention;

[0033]FIG. 3C is a perspective view of a shaft centerline offsetmeasurement device according to the present invention;

[0034]FIG. 4A is a front elevation view of the shaft centerline offsetmeasurement device in FIG. 3C;

[0035]FIG. 4B is a rear elevation view of the shaft centerline offsetmeasurement device in FIG. 3C;

[0036]FIG. 4C is a top plan view of the shaft centerline offsetmeasurement device in FIG. 3C;

[0037]FIG. 4D is a bottom plan view of the shaft centerline offsetmeasurement device in FIG. 3C;

[0038]FIG. 5A is a front elevation view of the shaft height measurementdevice in FIG. 3B;

[0039]FIG. 5B is a rear elevation view of the shaft height measurementdevice in FIG. 3B;

[0040]FIG. 5C is a top plan view of the shaft height measurement devicein FIG. 3B;

[0041]FIG. 5D is a bottom plan view of the shaft height measurementdevice in FIG. 3B;

[0042]FIGS. 6A and 6B are front and rear elevation views, respectively,of a shaft centerline offset measurement device mounted to a shaftwithin a vessel according to the present invention;

[0043]FIGS. 7A and 7B are front and rear elevation views, respectively,of a shaft height measurement device mounted to a shaft within a vesselaccording to the present invention;

[0044]FIGS. 8A, 8B and 8C are geometric views illustrating a method forcalculating the offset amount of the centerline of a shaft according tothe present invention;

[0045]FIG. 9 is a geometric view illustrating another method forcalculating the offset amount of the centerline of a shaft according tothe present invention;

[0046]FIGS. 10A and 10B are perspective views of a combined shaftcenterline offset and height measurement device according to the presentinvention;

[0047]FIGS. 11A and 11B are detailed perspective views of a shaftcenterline offset measurement module of the device in FIGS. 10A and 10B;

[0048]FIG. 12 is a detailed perspective view of a shaft heightmeasurement module of the device in FIGS. 10A and 10B; and

[0049]FIGS. 13A and 13B are a flow diagram of a test routine accordingto the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[0050]FIG. 1 illustrates a typical vessel V employed in a dissolutiontesting station, while FIG. 2 illustrates one such testing stationgenerally designated DTS. Vessel V has an open upper end 12, a lateralside region 14, and a hemispherical end region 16. A plurality ofvessels V (typically 6 or 8) are mounted in a rack 18 of dissolutiontesting station DTS for high-throughput testing. Each vessel V iscentered and locked into position on rack 18 with the aid of a vesselcentering ring CR (not shown in FIG. 2). Dissolution testing station DTSincludes, among other components, a water bath WB for temperaturecontrol of vessels V and a programmable systems control module 20 havingperipheral elements such as an LCD display 20A, a keypad 20B, andindividual readouts 20C. A shaft S provided with a paddle or basket Pmay be inserted into each vessel V. One or more spindle motors (notshown) housed within control module 20 drive the rotation of shafts Sthrough a chuck (not shown) or equivalent coupling means. Referringspecifically to FIG. 1, the parameters of shaft position relative tovessel V sought to be determined are shaft centerline offset determinedby shaft distance x, and shaft or paddle height y. The present inventiondescribed in detail below has been found by applicants to measure theseparameters accurately to within 0.1 mm.

[0051]FIGS. 3A through 3C show a shaft centerline offset and heightmeasurement system according to the present invention and generallydesignated 30. Primary components of measurement system include a shaftcenterline offset measurement device generally designated 40, a heightmeasurement device generally designated 50, and a control/displayconsole generally designated 60. Control/display console 60 is portableand thus includes a handle 60A. A keypad 60B is provided for inputtingcommands, calibration data, and the like. Results derived frommeasurements taken by centerline offset and height measurement devices40, 50 are transferred through electrical conduits EC and may bedisplayed at display screen 60C, which is preferably an LCD typedisplay. Alternatively, these results may be sent through acommunication port 60D such as an RS 232 port to another peripheral suchas a remote computer. Control/display console 60 can also be equippedwith an on-board dot-matrix printer 60E. In addition, control/displayconsole 60 includes a decoder chip adapted for decoding signal receivedfrom transducers, a CPU for performing calculations and other computingfunctions, a memory register, and other associated logic components andcircuitry (not shown). A suitable decoder chip is a quadrature decoderavailable from HEWLETT PACKARD as model designation HCTL-2016. Asuitable CPU is a micro controller unit available from PHILLIPS as modeldesignation 87C52.

[0052] Centerline offset measurement device 40 is illustrated in moredetail in FIGS. 3C and 4A through 4D. Height measurement device 50 isillustrated in more detail in FIGS. 3B and 5A through 5D.

[0053] Referring particularly to FIGS. 3C and 4A, centerline offsetmeasurement device 40 includes a housing 42, a lateral plunger 44, and ahorizontally-oriented sensor or transducer 46(indicated schematically inFIG. 4A by phantom lines). Preferably, both lateral plunger 44 andtransducer 46 are mounted within housing 42. Lateral plunger 44 ismovably mounted to housing 42 by conventional means, such that lateralplunger 44 can slide inwardly and outwardly with respect to housing 42.An outer section 44A of lateral plunger 44 extends outside housing 42through a hole 42A in a wall 42B of housing 42. Means such as a spring(not shown) is provided to interface with lateral plunger 44 and housing42 and to impart a biasing force to lateral plunger 44 in a radiallyoutward direction away from housing 42. Preferably, an arrow-shapedplunger head 44B is provided at a distal end 44C of lateral plunger 44for a purpose described hereinbelow. Means such as an electrical conduitEC containing lead wires is provided for transferring signals generatedby transducer 46.

[0054] Transducer 46 serves to measure a change in lateral position oflateral plunger 44 by converting a sense of the physical change in suchposition to an electronic signal representative of the magnitude of suchchange. For this purpose, transducer 46 is preferably an optical linearencoder module such as model designation HEDS 9200 R00 available fromHEWLETT PACKARD. Transducer 46 operates in conjunction with a code strip(not shown) in a manner typical of optical encoders. Because transducer46 is to measure positional changes of lateral plunger 44, the codestrip is mounted to an inner section 44D of lateral plunger 44 in thevicinity of transducer 46. Hence, as lateral plunger 44 moves, the codestrip moves with respect to transducer 46. As the code strip passes bytransducer 46, transducer 46 optically reads and counts lines on thecode strip. The number of lines counted is correlated to a magnitude bywhich lateral plunger 44 has moved from an initial reference position.Alternatively, transducer 46 could be mounted to lateral plunger 44 andthe code strip fixedly secured within housing 42.

[0055] Referring to FIGS. 3C, 4B and 4C, a longitudinal recess 48 isformed in a rear face 42C of housing 42 by a recess wall 48A.Preferably, recess wall 48A has a cylindrical profile to betteraccommodate the contour of shaft S. In an upper section 48B oflongitudinal recess 48 proximate to a top face 42D of housing 42, aclip-like member 49 is provided to assist the secure mounting of shaftcenterline offset measurement device 40 to shaft S. Clip-like member 49includes a pair of resilient prongs 49A and 49B. In addition, a bottomface 42E of housing 42 may be configured to conform to the specific typeof operative component, e.g., paddle or basket P, carried on shaft S inorder to further assist in mounting thereto. Thus, in the exemplaryembodiment shown in FIG. 4D, bottom face 42E includes a groove 42F thatenables housing 42 to straddle paddle P when mounted to shaft S. FIGS.6A and 6B show centerline offset measurement device 40 mounted to shaftS and shaft S installed in vessel V.

[0056] Referring particularly to FIGS. 3B and 5A, height measurementdevice 50 includes a housing 52, a vertical plunger 54, and avertically-oriented sensor or transducer 56 (indicated schematically inFIG. 5A by phantom lines). As in the case of centerline offsetmeasurement device 40, both vertical plunger 54 and transducer 56 arepreferably mounted within housing 52. Vertical plunger 54 is movablymounted to housing 52 by conventional means, such that vertical plunger54 can slide inwardly and outwardly with respect to housing 52. An outersection 54A of vertical plunger 54 extends outside housing 52 through ahole 52A in a wall 52B of housing 52. Means such as a spring (not shown)is provided to interface with vertical plunger 54 and housing 52 and toimpart a biasing force to vertical plunger 54 in a downward directionaway from housing 52. An end portion 54B is attached to vertical plunger54 in offset relation thereto by means of an intermediate member 54C.Accordingly, when height measurement device 50 is mounted to shaft S,vertical plunger 54 is situated in parallel relation to shaft S and endportion 54B is centrally disposed beneath shaft S and its operativecomponent P. The purpose of end portion 54B is described hereinbelow.Finally, means such as an electrical conduit EC containing lead wires isprovided for transferring signals generated by transducer 56.

[0057] In a manner analogous to that respecting centerline offsetmeasurement device 40, transducer 56 serves to measure a change invertical position of vertical plunger 54 by converting a sense of thephysical change in such position to an electronic signal representativeof the magnitude of such change. Consequently, transducer 56 specifiedfor height measurement device 50 is the same or similar unit astransducer 46 specified for centerline offset measurement device 40, aswell as the associated code strip which preferably is mounted tovertical plunger 54.

[0058] Referring to FIGS. 3B, 5B and 5C, means are provided for mountingheight measurement device 50 to shaft S similar to that respectingcenterline offset measurement device 40. That is, a longitudinal recess58 is formed in a rear face 52C of housing 52 by acylindrically-profiled recess wall 58A. A clip-like member 59 includinga pair of resilient prongs 59A and 59B is disposed in an upper section58B of longitudinal recess 58 proximate to a top face 52D of housing 52.In addition, a bottom face 52E of housing 52 includes a groove 52F orother means for improving the securement of height measurement device 50to shaft S provided with paddle P or the like, as shown in FIG. 5D.FIGS. 7A and 7B show height measurement device 50 mounted to shaft S andshaft S installed in vessel V.

[0059] The operation of shaft centerline offset and height measurementsystem 30 will now be described with particular reference to FIGS. 3A,6A, 6B, 7A, 7B, 8A through 8C, and 9. By way of example, an indicationof centerline offset is obtained before an indication of shaft or paddleheight is obtained.

[0060] Referring to FIGS. 6A and 6B, the operation of centerline shaftmeasurement device 40 will first be described. Centerline offsetmeasurement device 40 is affixed to shaft S. Shaft S is then loweredinto vessel V at a normal operating position for shaft S. Becauselateral plunger 44 is preferably biased radially outwardly, the taperededges that comprise arrow-shaped plunger head 44B assist in installingand removing shaft S from vessel V when centerline offset measurementdevice 40 is mounted to shaft S. After shaft S is disposed in its normaloperating position, a distal end (which in the present exemplaryembodiment corresponds to the outermost surface of plunger head 44B) ofoutwardly biased lateral plunger 44 is in contact with a lateral insidesurface ID of vessel V.

[0061] At this point, assuming shaft S is offset from the true centralvertical axis of vessel V, lateral plunger 44 will have displacedlaterally with respect to a zero reference position. At this plungerposition, lateral plunger 44 will have displaced a distance equal to adisplacement magnitude. This displacement magnitude is evident by thechange in position of the code strip mounted to lateral plunger 44.Transducer 46 encodes the displaced position of the code strip, and thusthe displaced position of lateral plunger 44, and sends the encodedsignal to control/display console 60 (see FIG. 3A), which decodes,stores, and processes the signal.

[0062] The displacement magnitude measured is one indication of theamount by which shaft S is offset from the central axis of vessel V.This displacement magnitude alone, however, is not necessarily a goodindication when one considers that the position of lateral plunger 44will change when lateral plunger 44 is disposed at other distal plungerpositions on the circumference of lateral inside surface ID of vessel V.Accordingly, more precision can be achieved by employing transducer 46to sample a plurality of displaced plunger positions. These displacedplunger positions are obtained when lateral plunger 44 is rotated todefine a plurality of distal plunger positions located on thecircumference of lateral inside surface ID. By doing so, a calculationof the centerline offset amount can be based on a plurality ofdisplacement magnitudes measured by transducer 46 at differentcircumferential locations on lateral inside surface ID.

[0063] Referring to FIGS. 8A through 8C, lateral inside surface ID isassumed to be a perfect circle ABC for purposes of calculation and has acenter O through which central axis of vessel V runs. The centerline ofthe shaft S is represented by a point T, thus illustrating that shaft Sis clearly not in alignment with the central axis of vessel V. Shaft Swith centerline offset measurement device 40 mounted thereto is insertedinto vessel V as described above, at which time distal end or plungerhead 44B of lateral plunger 44 contacts lateral inside surface ID at afirst distal plunger position A. The distance by which lateral plunger44 is displaced at this time is encoded by transducer 46 and stored incontrol/display console 60 as a first displacement magnitude. After thefirst displacement magnitude is measured, second and third displacementmagnitudes are likewise measured by respectively rotating lateralplunger 44 120° (or one-third of a revolution around lateral insidesurface ID) to a second distal plunger position B and another 120° to athird distal plunger position C.

[0064] Lateral plunger 44 can be rotated by manually rotating housing 42around shaft S or by rotating shaft S itself. In order to aid inlocating the 1200 positions, indicator marks (not shown) could beprovided, for instance, on vessel centering ring CR (see FIG. 1).Nevertheless, the method described herein will give an accurateindication of centerline offset even if readings are taken at plungerpositions that deviate approximately ±5° from the 120° positions.

[0065] Referring to FIG. 8A, a radial distance d₁, along lateral plunger44 from centerline T to first distal plunger position A, a radialdistance d₂ along lateral plunger 44 from centerline T to second distalplunger position B, and a radial distance d₃ along lateral plunger 44from centerline T to third distal plunger position C are obtained.Radial distances d₁, d₂ and d₃ can be derived in a variety of ways, suchas by taking a value representing some constant plunger length andadjusting that value by taking into account the measured first, secondand third displacement magnitudes, respectively. A chordal distance ABbetween first and second distal plunger positions A, B, a chordaldistance AC between first and third distal plunger positions A, C and achordal distance BC between second and third distal plunger positions B,C are then calculated respectively according to the following equationsderived from the law of cosines:${AB} = \sqrt{\left( d_{1} \right)^{2} + \left( d_{2} \right)^{2} - {2 \cdot d_{1} \cdot d_{2} \cdot {\cos \left( {\frac{2 \cdot \pi}{360} \cdot 120} \right)}}}$${AC} = \sqrt{\left( d_{1} \right)^{2} + \left( d_{3} \right)^{2} - {2 \cdot d_{1} \cdot d_{3} \cdot {\cos \left( {\frac{2 \cdot \pi}{360} \cdot 120} \right)}}}$${BC} = \sqrt{\left( d_{3} \right)^{2} + \left( d_{2} \right)^{2} - {2 \cdot d_{3} \cdot d_{2} \cdot {\cos \left( {\frac{2 \cdot \pi}{360} \cdot 120} \right)}}}$

[0066] Next, a theoretical radius R for circle ABC based on chordaldistances AB, AC, and BC is calculated according to the followingequation:$R = \frac{{AB} \cdot {AC} \cdot {BC}}{4 \cdot \sqrt{S \cdot \left( {S - {AB}} \right) \cdot \left( {S - {AC}} \right) \cdot \left( {S - {BC}} \right)}}$${{wherein}\quad {factor}\quad S} = \frac{{AB} + {AC} + {BC}}{2}$

[0067] Referring to FIG. 8B, it follows that radius R is equal to aradius AO from center O to first distal plunger position A, a radius BOfrom center O to second distal plunger position B, and a radius CO fromcenter O to third distal plunger position C. An angle AOB between radiiAO and BO is then calculated according to the following equation derivedfrom the law of cosines:${AOB} = {{\cos^{- 1}\left( \frac{({AO})^{2} + ({BO})^{2} - ({AB})^{2}}{{2 \cdot {AO} \cdot {BO}}\quad} \right)} \cdot \frac{360}{2 \cdot \pi}}$

[0068] Referring to FIG. 8C, values for radial distances AT and BT areequal to radial distances d₁ and d₂, respectively. Thus, an angle ABTbetween radial distances AT and BT is calculated according to thefollowing equation derived from the law of sines:${ABT} = {{\sin^{- 1}\left( \frac{d_{1} \cdot {\sin \left( \frac{120 \cdot 2 \cdot \pi}{360} \right)}}{AB} \right)} \cdot \frac{360}{2 \cdot \pi}}$

[0069] Next, an angle ABO between chordal distance AB and radius BO andan angle OBT between radius BO and radial distance BT are calculatedaccording to the following equations: ${ABO} = \frac{180 - {AOB}}{2}$

[0070] It will be seen from FIG. 8C that a triangle is defined by threevertices corresponding to center O, centerline T, and second distalplunger position B. Because the values for two sides of this triangle,radius BO and radial distance BT, and the angle OBT therebetween areknown, control/display console 60 can now calculate the value for theremaining side, which is the offset distance OT of centerline T fromcenter O. Offset distance OT is calculated according to the followingequation derived from the law of cosines:${OT} = \sqrt{({BO})^{2} + \left( d_{2} \right)^{2} - \left( {2 \cdot {BO} \cdot d_{2} \cdot {\cos \left( \frac{{OBT} \cdot 2 \cdot \pi}{360} \right)}} \right)}$

[0071] The offset distance OT provides an accurate indication of theamount by which the centerline of shaft S is offset from the centralaxis of vessel V in any radial direction. This is because thecalculation is based on three displacement magnitudes measured at threedifferent positions of lateral plunger 44 within vessel V, and therelationships between the various points and distances observed withinvessel V and described hereinabove can be resolved by trigonometricequations.

[0072] A preferred modification to the method described above yields thesame result, i.e., calculation of offset distance OT, yet avoids theadditional task of deriving values for radial distances AT, BT and CTfrom the first, second and third displacement magnitudes. In thispreferred modification, advantage is taken of the fact that the first,second and third displacement magnitudes measured by transducer 46 arelinearly proportional to radial distances AT, BT and CT, respectively.Thus, radial distance d₁ is set equal to zero, radial distance d₂ is setequal to a value based on the second displacement magnitude relative tothe first displacement magnitude, and radial distance d₃ is set equal toa value based on the third displacement magnitude relative to the firstdisplacement magnitude. For example, d₁=0, d₂=−0.1, and d₃=−0.9. If suchvalues for d₁, d₂ and d₃ are used and the above equations applied, thesame value for offset distance OT is obtained.

[0073] A further alternative method for calculating the amount by whichthe centerline of shaft S is offset from the central axis of vessel Vwill now be described with reference to FIG. 9. Lateral inside surfaceID of vessel V is represented by a circle AB in FIG. 9, and has a centerO through which the central axis of vessel V runs. The centerline ofshaft S is represented by point T. If a diameter for circle AB is drawnthrough center O and centerline T, it is observed that a maximumdisplacement magnitude will be measured when lateral plunger 44 isdisposed within vessel V along a maximum radial distance AT, and aminimum displacement magnitude will be measured when lateral plunger 44is rotated 180° and disposed along a minimum radial distance BT. Iflateral inside surface ID of vessel V were a perfect circle, an offsetdistance OT could be found by subtracting radius AO from radial distanceAT or by subtracting radial distance BT from radius BO. A preferredmethod of calculation, however, is derived as follows.

[0074] It is observed that maximum radial distance AT=AO+OT and minimumradial distance BT=BO−OT. For purposes of calculation, lateral insidesurface ID of vessel V is assumed to be a perfect circle such thatAO=BO. Thus, minimum radial distance BT=AO−OT. Offset distance OT can befound by subtracting maximum radial distance AT from minimum radialdistance BT as follows:

AT−BT=(AO+OT)−(AO−OT)=2OT

[0075] Therefore,${OT} = {\frac{\left( {{AO} + {OT}} \right) - \left( {{AO} - {OT}} \right)}{2} = \frac{{AT} - {BT}}{2}}$

[0076] In order to implement this method, lateral plunger 44 is rotated360°, i.e., one full revolution around the inside of vessel V. Atpredetermined intervals while lateral plunger 44 is rotating, e.g.,every 5 ms, transducer 46 encodes the position of lateral plunger 44 togenerate a data set consisting of a plurality of displacementmagnitudes. From this data set, a maximum measured displacementmagnitude d_(MAX) and a minimum measured displacement magnitude d_(MIN)are selected. An example of a subroutine that could perform thisselection process can be constructed from the following steps:

[0077] 1) READ a first displacement magnitude and STORE;

[0078] 2) READ a second displacement magnitude and STORE;

[0079] 3) IF second displacement magnitude<first displacement magnitude,THEN SET second displacement magnitude=d _(MIN) AND SET firstdisplacement magnitude=d_(MAX), ELSE SET second displacementmagnitude=d_(MAX) AND SET first displacement magnitude=d_(MIN);

[0080] 4) READ a third displacement magnitude;

[0081] 5) IF third displacement magnitude<d_(MIN) THEN SET thirddisplacement magnitude=d_(MIN);

[0082] 6) IF third displacement magnitude>d_(MAX) THEN SET thirddisplacement magnitude=d_(MAX).

[0083] This procedure is repeated successively until each sampleddisplacement magnitude is determined to be either the maximum or minimumfor the data set. Offset distance OT is then calculated according to thefollowing equation: ${OT} = \frac{d_{MAX} - d_{MIN}}{2}$

[0084] Referring primarily to FIGS. 7A and 7B, the operation of heightmeasurement device 50 will now be described. Height measurement device50 is affixed to shaft S. Prior to installation of shaft S in vessel V,a spherical object such as a stainless steel ball 65 having apredetermined uniform diameter is placed into vessel V. Stainless steelball 65 will come to rest at a lowermost point 19 on the inside surfaceof hemispherical end region 16 of vessel V, thereby locating the truebottom of vessel V. Vertical plunger 54 is biased to a fully downwardlyextended position. In order to obtain a zero reference position, endportion 54B of vertical plunger 54 is urged upwardly until good contactis made with the underside of paddle P or other operative component ofshaft S. Shaft S is then inserted into vessel V at a normal operatingposition for shaft S.

[0085] Once shaft S has been installed, vertical plunger 54 movesdownwardly until coming into contact with stainless steel ball 65. Atthis point, vertical plunger 54 will have displaced vertically withrespect to the zero reference position. The distance by which verticalplunger 54 displaces is characterized as its displacement magnitude.Transducer 56 encodes the displaced position by reading the code stripmounted to vertical plunger 54 and generates a signal representative ofthe measured displacement magnitude, in a manner analogous to theinteraction of transducer 46 and the code strip of lateral plunger 44 ofcenterline offset measurement device 40 described hereinabove.Transducer 56 sends the encoded signal to control/display console 60(see FIG. 3A). The height of paddle P above lowermost point 19 ofhemispherical end region 16 is most easily derived from the measureddisplacement magnitude by adding together the values for thedisplacement magnitude, the height of end portion 54B and the diameterof stainless steel ball 65.

[0086] As an alternative embodiment of the present invention, shaftcenterline offset and height measurement system 30 can be modified toincorporate both the shaft centerline offset and height measurementfunctions in a single measurement device. That is, housing 42 or 52 canbe adapted to accommodate both transducers 46 and 56, plungers 44 and54, and their associated components described hereinabove. However, apreferred approach to this functional combination is to provide a moremodular device which does not require the mounting of a single (andbulkier and heavier) housing to shaft S.

[0087] This preferred alternative embodiment will now be described withreference to FIGS. 10A, 10B, 11A, 11B and 12, illustrating a combinedshaft centerline offset and height measurement device generallydesignated 70.

[0088] Instead of employing a housing to serve as a mounting assemblyfor centralizing the operative components of the present embodiment, amodified vessel centering ring 75 is provided. Modified vessel centeringring 75 includes a central region 75A having a bore 75B through whichshaft S with paddle P or the like can be inserted.

[0089] Combined shaft centerline offset and height measurement device 70includes a centerline offset measurement module generally designated 80and a height measurement module generally designated 90. It will benoted that all operative components of combined shaft centerline andoffset measuring device 70, including centerline offset measurementmodule 80 and a height measurement module 90, are mounted directly orindirectly to modified vessel centering ring 75, and thus operateindependently of shaft S. Thus, while only one centerline offsetmeasurement module 80 could be provided and rotated by means such as aturntable mounted to modified vessel centering ring 75, it is moreadvantageous to provide three centerline offset measurement modules 80,all of which are suspended from modified vessel centering ring 75independently of shaft S. Moreover, as shown in FIGS. 10A and 10B,centerline offset measurement modules 80 are oriented 120° from eachother, thereby eliminating the alignment and rotation steps attendingcenterline offset measurement device 40 in FIGS. 4A through 4D.

[0090] Referring to FIGS. 11A and 11B, each centerline offset measuringmodule 80 includes a sensor body 82 which serves as a mounting bracketfor a lateral plunger 84 and a transducer 86. Sensor body 82 preferablyhas a U-shaped profile defined by a central region 82A and legs 82B and82C. Transducer 86 is preferably secured directly to the inside of leg82B of sensor body 82, and preferably is an optical linear encodersimilar to transducers 46 and 56. An upper linear bearing 102A isattached to a top surface 82D of central region 82A and a lower linearbearing 104A is attached to an end 82E of leg 82C. A lower bearing track104B is attached to each lateral plunger 84 and engages lower linearbearing 104A, thereby enabling lateral plunger 84 to slide laterallywith respect to sensor body 82. A code strip 106 is fixedly secured tolateral plunger 84 to cooperate with transducer 86 in the mannerdescribed hereinabove.

[0091] As shown in FIG. 10B, three upper bearing tracks 102B (of whichonly two are shown) are attached to central region 75A of modifiedvessel centering ring 75. Upper linear bearing 102A of each sensor body82 engages a corresponding upper bearing track 102B to enable eachsensor body 82 to slide laterally with respect to modified vesselcentering ring 75. In the exemplary embodiment shown in FIGS. 10A and10B, means such as springs (not shown) are provided respectively forbiasing each lateral plunger 84 radially inwardly and for biasing eachsensor body 82 radially outwardly. Thus, when shaft S is installed intovessel V, plunger tips 84A of lateral plungers 84 are biased to contactshaft S while rear faces 82F of sensor bodies 82 are biased to contactlateral inside surface ID of vessel V. Each lateral plunger 84 has upperand lower guide members 84B and 84C, respectively, to assist in urginglateral plungers 84 outwardly when shaft S is being inserted and removedfrom vessel V.

[0092]FIG. 12 is a detailed view of height measurement module 90, whichis an alternative to incorporating the structure of height measurementdevice 50 described hereinabove. Height measurement module 90 includes asensor mounting bracket 92, a vertical plunger 94, and avertically-oriented transducer 96. Vertical plunger 94 preferablyincludes a vertical rail 94A, an upper arm 94B, and a lower arm 94C.Sensor mounting bracket 92 includes a clamping section 92A by whichsensor mounting bracket 92 is fixedly secured to vertical rail 94A, suchas by inserting vertical rail 94A through clamping section 92A andtightening clamping section 92A with a fastener (not shown) threadedinto holes 92B.

[0093] In the preferred embodiment, lower arm 94C includes an arcuatesection 94CA and a lower end portion 94CB extending horizontally fromarcuate section 94CA. Likewise, upper arm 94B includes an arcuatesection 94BA and a lower end portion 94BB extending horizontally fromarcuate section 94BA. Arcuate sections 94BA and 94CA are disposedadjacent to each other, and upper end portion 94BB is disposed abovelower end portion 94CB. Means such as a spring 98 is connected betweenupper end portion 94BB and lower end portion 94CB in order to verticallybias upper and lower end 94BB and 94CB portions away from each other.

[0094] Lower arm 94C is secured to sensor mounting bracket 92, orpreferably is secured directly to vertical arm 94A such as by insertingvertical arm 94A into an upper portion of lower arm 94CC and employingfastening means similar to clamping section 92A. Upper arm 94B ismounted to an annular bearing 99 through which vertical rail 94Aextends, thus enabling upper arm 94B to move vertically with respect tolower arm 94C and transducer 96. Vertical rail 94A is provided with alongitudinal groove 94A′ which engages a complementary tongue (notshown) disposed within annular bearing 99, thereby preventing annularbearing 99 and upper arm 94B from rotating around vertical rail 94A.Upper arm 94B includes a recessed area 94BC into which a code strip (notshown) is attached to cooperate with transducer 96.

[0095] Vertical rail 94A is movably attached to modified vesselcentering ring 75 in order to render combined shaft centerline offsetand height measurement device 70 compatible with vessels V of differentsizes. Preferably, an annular bearing (not shown) similar to annularbearing 99 is attached to modified vessel centering ring 75 and verticalrail 94A is extended therethrough. In addition, means such as a spring(not shown) is provided to bias vertical rail 94A (and thus heightmeasurement module 90 in its entirety) downwardly.

[0096] To complete the measurement system, it will be readily apparentthat combined shaft centerline and offset measurement device 70 isoperable in conjunction with control/display console 60 in FIG. 3A,although some reprogramming is necessary. Combined shaft centerline andoffset measurement device 70 can be made to communicate withcontrol/display console 60 by running appropriate data lines such asconduits EC from transducers 86, 96 to control/display console 60.

[0097] The operation of combined shaft centerline and offset measurementdevice 70 will now be described. Stainless steel ball 65 is insertedinto vessel V in order to locate lowermost point 19 of hemispherical endregion 16. Modified vessel centering ring 75, equipped with combinedshaft centerline and offset measurement device 70, is then fitted ontorack 18 of dissolution testing station DTS over one of vessels V. Atthis time, rear face 82F of radially outwardly biased sensor body 82 ofeach centerline offset measurement module 80 makes contact with lateralinside surface ID of vessel V. Additionally, lower end portion 94CB ofdownwardly biased vertical plunger 94 of height measurement module 90makes contact with stainless steel ball 65.

[0098] Shaft S is then lowered into vessel V to its normal operatingposition. Shaft S passes through bore 75B of modified vessel centeringring 75 while being lowered into vessel V. Also, paddle P contacts oneor more upper guide members 84B of lateral plungers 84 while shaft S isbeing lowered into vessel V, thus urging one or more of lateral plungers84 outwardly to clear the way for paddle P to pass downwardly. Onceshaft S reaches its normal operating position, plunger tips 84A ofradially inwardly biased lateral plungers 84 are in full contact withshaft S.

[0099] Assuming shaft S is offset from the central axis of vessel V, oneor more of lateral plungers 84 of centerline offset measurement modules80 will have displaced outwardly with respect to a predetermined zeroreference position for displaced lateral plunger or plungers 84. Hence,lateral plungers 84 operate in a manner analogous to lateral plunger 44of centerline offset measurement device 40. Each lateral plunger 84 ifdisplaced will have moved by a distance equal to a displacementmagnitude along the radial direction of that particular lateral plunger84. This physical event is measured and converted into an electricalsignal by the coaction of transducer 86 and its associated code strip106 as described hereinabove. Accordingly, three signals representingthe displacement magnitudes at the 120° positions along lateral insidesurface ID of vessel V are sent to control/display console 60. Offsetdistance OT is then preferably calculated by employing the sequence ofsteps including the trigonometric equations described hereinabove.

[0100] Height measurement module 90 also operates when shaft S isinstalled in vessel V. Before the bottom end of shaft S or its paddle Preaches its lowermost position within vessel V, upper end portion 94BBof upper arm 94B of vertical plunger 94 is biased in its highestposition above lower end portion 94CB of lower arm 94C. This constitutesa zero reference position for vertical plunger 94. As shaft S is beinglowered into vessel V, paddle P makes contact with upper end portion94BB. By the time shaft S reaches its final, normal operating position,paddle P will have urged upper end portion 94BB downwardly towards lowerend portion 94CB against the biasing force of spring 98. As the codestrip for vertical plunger 94 is fixedly mounted in recessed area 94BCof upper arm 94B, the code strip moves downwardly by the same distanceas upper end portion 94BB. This distance constitutes the displacementmagnitude for vertical plunger 94, which is encoded by transducer 96,and a signal is sent to control/display console 60 for furtherprocessing. One way to derive or interpret the height of paddle P abovelowermost point 19 of vessel V is to add together values for themeasured displacement magnitude, the height of upper end portion 94BB,the height of lower end portion 94CB, and the diameter of stainlesssteel ball 65.

[0101] It will be understood that while the Figures depictcontrol/display console 60 as being portable and designed for remoteoperation, the present invention encompasses a variation whereincontrol/display console 60 is integrated into dissolution testingstation DTS. For example, the operative components of control/displayconsole 60 can be housed within programmable systems control module 20of dissolution testing station DTS (see FIG. 2).

[0102]FIGS. 13A and 13B illustrate by way of example a flow diagram of atest routine executable by software written for control/display console60. The particular test routine illustrated manages the operation ofshaft centerline offset and height measurement system 30 with centerlineoffset measurement device 40 and height measurement device 50. It willbe understood, however, that the software can be rewritten without undueexperimentation and adapted for use of control/display console 60 withcombined shaft centerline offset and height measurement device 70. It isalso to be noted that this test routine can be configured, for example,to test up to 30 dissolution testing stations DTS and up to 8 shafts Sand corresponding vessels V per dissolution testing station DTS.Therefore, a total of 240 shaft sites can be tested in a single testroutine if desired.

[0103] Referring again to FIGS. 13A and 13B, display screen 60C ofcontrol/display console 60 displays a main menu at step 115, promptingthe user to select either a test run for shaft height measurement or atest run for shaft offset measurement. If the user selects a test runfor shaft height measurement, a shaft height measurement subroutine120-137 is initiated. On the other hand, if the user selects a test runfor shaft offset (or “ctr line”) measurement, a shaft offset measurementsubroutine 140-157 is initiated.

[0104] When the shaft height measurement subroutine is initiated, theuser is prompted at step 120 to assign an integer from 1 to 30 to thedissolution testing station presently being tested in order todistinguish that testing station from other testing stations to betested. The user is then prompted at step 125 to input an identificationfor that particular testing station, such as a serial number. Shaftsoperating in that testing station are assigned numbers according to therespective positions of the shafts in the testing station, such as 1through 6 or 1 through 8. Thus, the user is prompted at step 130 toeither initiate testing of a particular shaft, proceed to the nextshaft, or exit the shaft height measurement subroutine and return to themain menu.

[0105] If the user desires to test that particular shaft, the user isprompted at step 131 to input an identification for the shaft, such as aserial number. Next, the user is prompted at step 132 to input anidentification for the vessel in which the shaft operates. The user isthen prompted to place the stainless steel ball into the vessel at step133, install the shaft height measurement device at step 134, press thevertical plunger upwardly against the paddle or basket of the shaft inorder to obtain a zero reference reading at step 135, and lower theshaft equipped with the height measurement device into the vessel atstep 136. Once the shaft height measurement has been taken andappropriately interpreted, a readout or indication of the shaft heightis displayed at step 137 and the user is prompted to test another shaftin the particular testing station being tested.

[0106] When the shaft centerline offset measurement subroutine isinitiated by selection at step 115, the user is prompted at step 140 toassign an integer to the dissolution testing station presently beingtested. The user is then prompted at step 145 to input an identificationfor that particular testing station. Next, the user is prompted at step150 to either initiate testing of a particular shaft identified by itsposition number, proceed to the next shaft, or exit the shaft centerlineoffset measurement subroutine and return to the main menu.

[0107] If the user desires to test that particular shaft, the user isprompted at step 151 to input an identification for the shaft. Next, theuser is prompted at step 152 to input an identification for the vesselin which the shaft operates. The user is then prompted to install theshaft centerline offset measurement device at step 153, and to lower theshaft equipped with the offset measurement device into the vessel atstep 154. After a key input is entered at this position, the user isprompted at step 155 to rotate the shaft 120°. A key input is requestedto indicate the completion of this step. The user is then prompted atstep 156 to rotate the shaft another 120°, and a key input is requestedto indicate the completion of this step. Once the measurements taken atthese positions have been appropriately interpreted and the offsetdistance calculated, a readout or indication of the shaft centerlineoffset is displayed at step 157 and the user is prompted to test anothershaft in the particular testing station being tested.

[0108] These steps are repeated for every shaft and dissolution testingstation desired by the user to be tested.

[0109] It will be understood that in the case where the centerlineoffset is measured by making one full rotation around the vessel inorder to sample a plurality of displacements, the steps of the testroutine are modified accordingly. It will also be understood that in thecase where a testing routine such as that just described is adapted foruse in conjunction with combined shaft centerline offset and heightmeasurement device 70, the total number of steps required by the testroutine can be reduced.

[0110] It will be further understood that various details of theinvention may be changed without departing from the scope of theinvention. Furthermore, the foregoing description is for the purpose ofillustration only, and not for the purpose of limitation--the inventionbeing defined by the claims.

What is claimed is:
 1. An apparatus mountable to a shaft disposed within a vessel and adapted for measuring the magnitude by which the centerline of the shaft is offset from the central axis of the vessel, comprising: (a) a housing; (b) a plunger slidably mounted to the housing, the plunger having an outer section extending radially outwardly beyond a wall of the housing, and having means for biasing the plunger radially outwardly; (c) a transducer operatively mounted to the housing and adapted to encode positions of the plunger and to produce an electrical signal proportional to a change in position resulting from displacement of the plunger; and (d) means for transferring the signal to means for interpreting the signal.
 2. The apparatus according to claim 1 wherein the housing includes a rear face and a longitudinal recess defined by a recess wall extending inwardly toward an interior of the housing from the rear face.
 3. The apparatus according to claim 2 wherein the recess wall has a cylindrical profile.
 4. The apparatus according to claim 2 wherein the longitudinal recess includes an upper section extending downwardly from a top face of the housing, the upper section having a width greater than a width of an adjacent section of the longitudinal recess, the apparatus further comprising means disposed in the upper section for removably securing the housing to the shaft.
 5. The apparatus according to claim 4 wherein the removably securing means includes a clip extending outwardly from the recess wall within the upper section, the clip including a pair of resilient prongs.
 6. The apparatus according to claim 5 wherein each prong has an inside surface, and the clip and inside surfaces of the prongs cooperatively define a cylindrical profile.
 7. The apparatus according to claim 1 wherein the housing has a bottom face and a groove extending inwardly toward an interior of the housing from the bottom face.
 8. The apparatus according to claim 1 wherein the plunger is slidably disposed within the housing and the outer section of the plunger extends radially outwardly through a hole in the wall of the housing.
 9. The apparatus according to claim 1 further comprising a plate mounted to the plunger and including a plurality of equally spaced lines readable by the transducer, wherein the transducer is an optical encoder disposed within the housing and the number of lines read by the transducer corresponds to a magnitude of the change in position of the plunger.
 10. The apparatus according to claim 1 wherein the signal transferring means includes an electrical conduit and the signal interpreting means includes a console disposed in remote relation to the housing, wherein the electrical conduit communicates with the console.
 11. An apparatus mountable to a shaft having a paddle or basket disposed within a vessel, the vessel having a central axis and a hemispherical end region, the apparatus adapted for measuring the distance from a distal surface of the paddle or basket to a lowermost point on the inside surface of the hemispherical end region and comprising: (a) a housing; (b) a plunger slidably mounted to the housing, the plunger having an outer section extending outwardly beyond a wall of the housing, means for biasing the plunger outwardly, and an end portion extending transversely from the plunger beneath the housing and substantially centered about a central portion of the housing; (c) a transducer operatively mounted to the housing and adapted to encode positions of the plunger and to produce an electrical signal proportional to a change in position resulting from displacement of the plunger; and (d) means for transferring the signal to means for interpreting the signal.
 12. The apparatus according to claim 11 wherein the housing includes a rear face and a longitudinal recess defined by a recess wall extending inwardly toward an interior of the housing from the rear face.
 13. The apparatus according to claim 12 wherein the recess wall has a cylindrical profile.
 14. The apparatus according to claim 12 wherein the longitudinal recess includes an upper section extending downwardly from a top face of the housing, the upper section having a width greater than a width of an adjacent section of the longitudinal recess, the apparatus further comprising means disposed in the upper section for removably securing the housing to the shaft.
 15. The apparatus according to claim 4 wherein the removably securing means includes a clip extending outwardly from the recess wall within the upper section, the clip including a pair of resilient prongs.
 16. The apparatus according to claim 15 wherein each prong has an inside surface, and the clip and inside surfaces of the prongs cooperatively define a cylindrical profile.
 17. The apparatus according to claim 11 wherein the housing has a bottom face and a groove extending inwardly toward an interior of the housing from the bottom face.
 18. The apparatus according to claim 11 wherein the plunger is slidably disposed within the housing and the outer section of the plunger extends outwardly through a hole in the wall of the housing.
 19. The apparatus according to claim 11 further comprising a plate mounted to the plunger and including a plurality of equally spaced lines readable by the transducer, wherein the transducer is an optical encoder disposed within the housing and the number of lines read by the transducer corresponds to a magnitude of the change in position of the plunger.
 20. The apparatus according to claim 11 wherein the signal transferring means includes a electrical conduit and the signal interpreting means includes a console disposed in remote relation to the housing, wherein the electrical conduit communicates with the console.
 21. A system for determining the location of a rotatable shaft in relation to a vessel, the vessel mounted to a rack of a dissolution testing station, the shaft having a first end mounted to the testing station above the vessel, a second end disposed within the vessel and an operative component secured to the second end, the system comprising: (a) a housing including means for removably mounting the housing to the shaft; (b) a plunger slidably mounted to the housing, the plunger having an outer section extending radially outwardly beyond a wall of the housing and extendable to an inside lateral surface of the vessel, and having means for biasing the plunger radially outwardly; (c) a transducer operatively mounted to the housing, the transducer adapted to encode positions of the plunger and to produce an electrical signal proportional to a distance from a reference position to an extended position at which the plunger is in contact with the inside lateral surface of the vessel; and (d) means for transferring the signal to means for interpreting the signal.
 22. A system for determining the location of a rotatable shaft in relation to a vessel, the vessel having a central axis and a hemispherical end region and mounted to a rack of a dissolution testing station, the shaft having a first end mounted to the testing station above the vessel, a second end disposed within the vessel and an operative component secured to the second end, the system comprising: (a) a spherical object removably disposed in a lowermost point on an inside surface of the hemispherical end region of the vessel; (b) a housing including means for removably mounting the housing to the shaft; (c) a plunger slidably mounted to the housing, the plunger having an outer section extending beyond a wall of the housing and extendable to the spherical object, means for biasing the plunger outwardly, and an end portion having an upper surface and a lower surface, the end portion extending transversely from the plunger and between the operative component and the spherical object; (d) a transducer operatively mounted to the housing, the transducer adapted to encode positions of the plunger and to produce an electrical signal proportional to a distance from a reference position at which the top surface of the end portion of the plunger is biased against the operative component to an extended position at which the lower surface is in contact with the spherical object; and (e) means for transferring the signal to means for interpreting the signal.
 23. A system for determining the location of a shaft in relation to a vessel in which the shaft is disposed, the vessel having a central axis and a hemispherical end region, the system comprising: (a) a shaft offset measurement device including: (i) a first housing; (ii) a first plunger slidably mounted to the first housing, the first plunger having an outer section extending radially outwardly beyond a wall of the first housing, and having means for biasing the first plunger radially outwardly; and (iii) a first transducer operatively mounted to the first housing and adapted to encode positions of the first plunger and to produce a first electrical signal proportional to a change in position resulting from displacement of the first plunger; (b) a shaft height measurement device including: (i) a second housing; (ii) a second plunger slidably mounted to the second housing, the second plunger having an outer section extending outwardly beyond a wall of the second housing, means for biasing the second plunger outwardly, and an end portion extending transversely from the second plunger beneath the second housing and substantially centered about a central portion of the second housing; and (iii) a second transducer operatively mounted to the second housing and adapted to encode positions of the second plunger and to produce a second electrical signal proportional to a change in position resulting from displacement of the second plunger; (d) a console including logic means for effecting interpretations of the first and second electrical signals and means for displaying the interpretations in human-readable form; and (e) means for transferring the first and second signals to the logic means.
 24. An apparatus adapted for measuring the magnitude by which the centerline of a shaft is offset from the central axis of a vessel in which the shaft is disposed, and for measuring the distance from a distal end of the shaft to the lowermost point on an inside surface of a hemispherical end region of the vessel, the apparatus comprising: (a) a mounting assembly; (b) a lateral plunger slidably mounted to the mounting assembly and having means for biasing the lateral plunger radially outwardly; (c) a lateral transducer operatively disposed with respect to the mounting assembly and to the lateral plunger, the lateral transducer adapted to encode positions of the lateral plunger and to produce an electrical signal proportional to a change in position resulting from displacement of the lateral plunger; (d) a vertical plunger slidably mounted to the mounting assembly, the vertical plunger having means for biasing the vertical plunger downwardly with respect to the mounting assembly and including an upper end portion extending transversely from the vertical plunger; (e) a vertical transducer operatively disposed with respect to the mounting assembly and to the vertical plunger, the vertical transducer adapted to encode positions of the vertical plunger and to produce an electrical signal proportional to a change in position resulting from displacement of the vertical plunger; and (f) means for transferring the signals produced respectively by the lateral and vertical transducers to means for interpreting the signals.
 25. The apparatus according to claim 24 wherein the mounting assembly includes a centering ring.
 26. The apparatus according to claim 24 further comprising a lateral mounting bracket attached to the mounting assembly, wherein the lateral plunger is slidably mounted to the lateral mounting bracket.
 27. The apparatus according to claim 26 wherein the lateral mounting bracket includes a lower bearing member and the lateral plunger includes a lower bearing track slidably mounted to the lower bearing member, and the apparatus further comprises means for biasing the lateral plunger inwardly with respect to the lateral mounting bracket.
 28. The apparatus according to claim 26 wherein the lateral transducer is mounted to the lateral mounting bracket and the apparatus further comprises a code strip, the code strip mounted to the lateral plunger and slidable with the lateral plunger in operative relation to the lateral transducer.
 29. The apparatus according to claim 26 wherein the mounting assembly includes an upper bearing track, the lateral mounting bracket includes an upper bearing member disposed in movable engagement with the upper bearing track, and the means for biasing the lateral plunger radially outwardly is a means for biasing the lateral mounting bracket radially outwardly along the upper bearing track.
 30. The apparatus according to claim 24 further comprising a code strip mounted to the lateral plunger and slidable with the lateral plunger in operative relation to the lateral transducer.
 31. The apparatus according to claim 24 further comprising a plurality of lateral plungers and a plurality of corresponding lateral transducers.
 32. The apparatus according to claim 31 wherein the plurality of lateral plungers are three in number, the plurality of corresponding lateral transducers are three in number, and each lateral plunger is disposed 120° from the other lateral plungers.
 33. The apparatus according to claim 24 further comprising a code strip mounted to the vertical plunger and slidable with the vertical plunger in operative relation to the vertical transducer.
 34. The apparatus according to claim 24 further comprising a linear bearing mounted to the mounting assembly, wherein the vertical plunger is mounted to the linear bearing.
 35. The apparatus according to claim 24 wherein the vertical plunger includes a first arm and a second arm, the second arm slidably mounted to the mounting assembly, wherein the upper end portion of the vertical plunger extends transversely from the first arm and the second arm includes a lower end portion extending transversely from the second arm below the upper end portion, the apparatus further comprising means for slidably mounting the first arm in relation to the second arm and means for biasing the upper end portion in spaced-apart relation to the lower end portion.
 36. The apparatus according to claim 35 further comprising a vertical transducer mounting bracket secured to the second arm, wherein the vertical transducer is attached to the vertical transducer mounting bracket.
 37. The apparatus according to claim 36 further comprising a code strip mounted to the first arm and slidable with the first arm in operative relation to the vertical transducer.
 38. The apparatus according to claim 35 wherein the first arm includes a first arcuate section, the upper end portion extends transversely from the first arcuate section, the second arm includes a second arcuate section disposed substantially adjacent to the first arcuate section, and the lower end portion extends transversely from the second arcuate section.
 39. The apparatus according to claim 35 further comprising a first linear bearing attached to the mounting assembly and a vertical rail slidably mounted to the first linear bearing, wherein the second arm is mounted to the vertical rail and depends downwardly therefrom, the means for slidably mounting the first arm in relation to the second arm includes a second linear bearing movably connected to the vertical rail, the first arm is attached to the second linear bearing, and the means for biasing the plunger downwardly is disposed in operative communication with the vertical rail.
 40. The apparatus according to claim 39 further comprising a vertical transducer mounting bracket connected to the vertical rail, wherein the vertical transducer is attached to the vertical transducer mounting bracket.
 41. The apparatus according to claim 40 wherein the second arm is mounted to the vertical transducer mounting bracket and depends downwardly below the vertical transducer mounting bracket and the vertical rail.
 42. The apparatus according to claim 24 wherein the signal interpreting means includes a console having logic means for effecting interpretations of the signals produced respectively by the lateral and vertical transducers and having means for displaying the interpretations in human-readable form, and wherein the signal transferring means communicates with the console.
 43. The apparatus according to claim 24 wherein the mounting assembly has a bore and is mounted over an open end of the vessel, and the shaft is insertable into the vessel through the bore.
 44. A method for measuring the amount by which the centerline of a shaft is offset from the central axis of a vessel in which the shaft is to be disposed, comprising the steps of: (a) mounting a measurement device including a radially outwardly biased plunger to the shaft, the plunger having a settable zero reference position; (b) inserting the shaft into the vessel at a normal operating position of the shaft, wherein a distal end of the plunger is in contact with a lateral inside surface of the vessel at a first distal plunger position; (c) defining a first displaced plunger position as a position on the plunger located a distance by which the plunger has moved in relation to the zero reference position, the distance being equal a first displacement magnitude; (d) measuring the first displacement magnitude by encoding the first displaced plunger position and interpreting the first displaced plunger position in relation to the zero reference position, wherein the first displacement magnitude is proportional to the shaft centerline offset amount; (e) calculating a value for the shaft centerline offset amount based on the measured first displacement magnitude; and (f) producing a signal indicative of the shaft centerline offset amount.
 45. The method according to claim 44 further comprising the steps of: (a) rotating the measurement device 120° after measuring the first displacement magnitude, wherein the distal end of the plunger is in contact with the lateral inside surface of the vessel at a second distal plunger position; (b) defining a second displaced plunger position as a position on the plunger located a distance by which the plunger has moved in relation to the zero reference position, the distance being equal to a second displacement magnitude; (c) measuring the second displacement magnitude by encoding the second displaced plunger position and interpreting the second displaced plunger position in relation to the zero reference position; (d) rotating the measurement device 120° after measuring the second displacement magnitude, wherein the distal end is in contact with the lateral inside surface at a third distal plunger position (e) defining a third displaced plunger position as a position on the plunger located a distance by which the plunger has moved in relation to the zero reference position, the distance being equal to a third displacement magnitude; (f) measuring the third displacement magnitude by encoding the third displaced plunger position and interpreting the third displaced plunger position in relation to the zero reference position; and (g) wherein the step of calculating the shaft centerline offset amount is based on the measured first, second and third displacement magnitudes.
 46. The method according to claim 45 wherein the step of calculating the shaft centerline offset amount includes the steps of: (a) calculating a first value AB according to a first equation: AB={square root}{square root over ((d ₁)²+(d ₂)²−2·d ₁ ·d ₂·cos(2·π/360·120))},  wherein d₁ is taken as equal to zero and d₂ is equal to a value for the measured second displacement magnitude relative to the measured first displacement magnitude; (c) calculating a second value AC according to a second equation: AC={square root}{square root over ((d ₁)²+(d ₃)²−2·d ₁ ·d ₃·cos(2·π/360·120))},  wherein d₃ is equal to a value for the measured third displacement magnitude relative to the measured first displacement magnitude; (d) calculating a third value BC according to a third equation: BC={square root}{square root over ((d ₃)²+(d ₂)²−2·d ₃ ·d ₂·cos(2·π/360·120))}; (e) calculating a fourth value R according to a fourth equation: R=AB·AC·BC/4·{square root}{square root over (S·(S−AB)·(S−AC)·(S−BC))}, wherein S=AB+AC+BC/2; (f) calculating a fifth value AOB according to a fifth equation: AOB=cos⁻¹((AO)²+(BO)²−(AB)²/2·AO·BO)·360/2·π; (g) calculating a sixth value ABT according to a sixth equation: ABT=sin⁻¹(d ₁·sin(120·2·π/360)/AB)·360/2·π; (h) calculating a seventh value ABO according to a seventh equation: ABO=180−AOB/2; (i) calculating an eighth value OBT according to an eighth equation: OBT=ABT−ABO; and (j) defining the shaft centerline offset amount as a distance OT according to a ninth equation: OT={square root}{square root over ((BO)²+(d ₂)²−(2·BO·d ₂·cos(OBT·2·π/360)))},  wherein the signal produced is indicative of the calculated distance OT.
 47. The method according to claim 45 wherein the step of calculating the shaft centerline offset amount includes the steps of: (a) defining the lateral inside surface of the vessel as being substantially coincident with a circle ABC, the circle ABC having points A, B and C, wherein the point A corresponds to the first distal plunger position, the point B corresponds to the second distal plunger position, and the point C corresponds to a third distal plunger position; (b) calculating a first chordal distance AB between the first and second distal plunger positions according to a first equation: AB={square root}{square root over ((d ₁)²+(d ₂)²−2·d ₁ ·d ₂·cos(2·π/360·120))},  wherein d₁ is equal to a first radial distance AT defined from the centerline of the shaft to the first distal plunger position and is linearly proportional to the measured first displacement magnitude, and d₂ is equal to a second radial distance BT defined from the centerline of the shaft to the second distal plunger position and is linearly proportional to the measured second displacement magnitude; (c) calculating a second chordal distance AC between the first and third distal plunger positions according to a second equation: AC={square root}{square root over ((d ₁)²+(d ₃)²−2·d ₁ ·d ₃·cos(2·π/360·120))};  wherein d₃ is equal to a third radial distance CT defined from the centerline of the shaft to the third distal plunger position and is linearly proportional to the measured third displacement magnitude; (d) calculating a third chordal distance BC between the second and third distal plunger positions according to a third equation: BC={square root}{square root over ((d ₃)²+(d ₂)²−2·d ₃ ·d ₂·cos(2·π/360·120))}, (e) calculating a theoretical radius R of the circle ABC according to a fourth equation: R=AB·AC·BC/4·{square root}{square root over (S·(S−AB)·(S−AC)·(S−BC))},  wherein S=AB+AC+BC/2; (f) calculating an angle AOB defined between a radius AO and a radius BO, the radius AO being defined as a radial distance from a theoretical center O of the circle ABC to the point A and the radius BO being defined as a radial distance from the theoretical center O to the point B, each of the radii AO and BO being taken as equal to the theoretical radius R, according to a fifth equation: AOB=cos⁻¹((AO)²+(BO)²−(AB)²/2·AO·BO)·360/2·π; (g) calculating an angle ABT defined between the first chordal distance AB and the radial distance BT according to a sixth equation: ABT=sin⁻¹(d ₁·sin(120·2·π/360)/AB)·360/2·π; (h) calculating an angle ABO defined between the first chordal distance AB and the radius BO according to a seventh equation: ABO=180−AOB/2; (i) calculating an angle OBT defined between the radius BO and the radial distance BT according to an eighth equation: OBT=ABT−ABO; and (j) defining the shaft centerline offset amount as a distance OT between the theoretical center O and the centerline of the shaft, and calculating the distance OT according to a ninth equation: OT={square root}{square root over ((BO)²+(d ₂)²−(2·BO·d ₂·cos(OBT·2·π/360)))},  wherein the signal produced is indicative of the calculated distance OT.
 48. The method according to claim 44 wherein: (a) the plunger is permitted to contact the lateral inside surface of the vessel at a plurality of distal plunger positions, wherein each distal plunger position is circumferentially spaced from the other distal plunger positions; (b) the step of defining the first displaced plunger position includes defining a plurality of displaced plunger positions in addition to the first displaced plunger position, each displaced plunger position being defined when the plunger is disposed at a corresponding one of the plurality of distal plunger positions, and the plurality of displaced plunger positions being positions on the plunger located a plurality of respective distances by which the plunger has moved in relation to the zero reference position, wherein each of the respective distances is equal to a corresponding one of a plurality of displacement magnitudes; (c) the step of measuring the first displacement magnitude includes measuring a plurality of displacement magnitudes in addition to the first displacement magnitude by encoding each of the displaced plunger positions in relation to the zero reference position; and (d) the step of calculating the value of the shaft centerline offset amount is based on the plurality of measured displacement magnitudes.
 49. The method according to claim 48 further comprising the steps of: (a) rotating the measurement device 360°; (b) measuring the first displacement magnitude and the plurality of displacement magnitudes by sampling, at predetermined time intervals while the measurement device is rotating, a reading from a transducer operatively disposed in relation to the plunger; (c) selecting the maximum measured displacement magnitude d_(MAX) and the minimum measured displacement magnitude d_(MIN); and (d) calculating a value OT equal to the shaft centerline offset amount according to the following equation: OT=d _(MAX) −d _(MIN)/2,  wherein the signal produced is indicative of the calculated value OT.
 50. The method according to claim 44 further comprising the step of displaying an indication of the shaft centerline offset amount in human-readable form.
 51. A method for measuring a shaft height defined as the distance between the distal end of a shaft and the inside lowermost surface of a hemispherical end region of a vessel in which the shaft is to be disposed, comprising the steps of: (a) mounting a measurement device including a downwardly biased plunger to the shaft, the plunger including an end portion extending below the shaft, the end portion having a predetermined end portion height; (b) defining a zero reference position of the plunger by urging the end portion against the distal end of the shaft and encoding the zero reference position; (c) locating the inside lowermost surface of the hemispherical end region of the vessel by inserting a spherical object having a predetermined diameter into the vessel; (d) inserting the shaft into the vessel at a normal operating position of the shaft; (e) permitting the end portion of the plunger to contact the spherical object; (f) defining a displaced plunger position as a position on the plunger located a distance by which the plunger has moved in relation to the zero reference position in order to contact the spherical object, the distance being equal to a displacement magnitude; (g) measuring the displacement magnitude by encoding the displaced plunger position and interpreting the displaced plunger position in relation to the zero reference position, wherein the displacement magnitude is proportional to the shaft height; (h) calculating a value for the shaft height based on the measured displacement magnitude; and (i) producing a signal indicative of the shaft height.
 52. The method according to claim 51 wherein the step of calculating a value for the shaft height includes adding the measured displacement magnitude to a first value representing the height of the end portion of the plunger and a second value representing the diameter of the spherical object.
 53. The method according to claim 51 further comprising the step of displaying an indication of the shaft height in human-readable form.
 54. A method for measuring the amount by which the centerline of a shaft is offset from the central axis of a vessel in which the shaft is to be disposed, and for measuring a shaft height defined as the distance between the distal end of the shaft and the inside lowermost surface of a hemispherical end region of the vessel, comprising the steps of: (a) locating the inside lowermost surface of the hemispherical end region of the vessel by inserting a spherical object into the vessel; (b) mounting a measurement device over the vessel, the measurement device including a lateral plunger and a vertical plunger, the vertical plunger including an end portion; (c) inserting the shaft into the vessel at a normal operating position of the shaft; (d) permitting a distal end of the lateral plunger to contact a lateral inside surface of the vessel; (e) defining a displaced lateral plunger position as a position on the lateral plunger located a lateral distance by which the lateral plunger has moved in relation to a settable zero reference position of the lateral plunger, the lateral distance being equal to a lateral displacement magnitude; (f) measuring the lateral displacement magnitude by encoding the displaced lateral plunger position and interpreting the displaced lateral plunger position in relation to the zero reference position of the lateral plunger, wherein the lateral displacement magnitude is proportional to the shaft centerline offset amount; (g) calculating a value for the shaft centerline offset amount based on the measured lateral displacement magnitude; (h) producing a signal indicative of the shaft centerline offset amount; (i) permitting the end portion of the vertical plunger to contact the spherical object; (j) defining a displaced vertical plunger position as a position on the vertical plunger located a vertical distance by which the vertical plunger has moved in relation to a predetermined zero reference position of the plunger, the vertical distance being equal to a vertical displacement magnitude; (k) measuring the vertical displacement magnitude by encoding the displaced vertical plunger position and interpreting the displaced vertical plunger position in relation to the zero reference position of the vertical plunger, wherein the vertical displacement magnitude is proportional to the shaft height; (l) calculating a value for the shaft height based on the measured vertical displacement magnitude; and (m) producing a signal indicative of the shaft height. 